The dimension subalgebra problem for enveloping algebras of Lie superalgebras
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- by David M. Riley PDF
- Proc. Amer. Math. Soc. 123 (1995), 2975-2980 Request permission
Abstract:
Let L be an arbitrary Lie superalgebra over a field of characteristic different from 2. Denote by $\omega u(L)$ the ideal generated by L in its universal enveloping algebra $U(L)$. It is shown that $L \cap \omega u{(L)^n} = {\gamma _n}(L)$ for each $n \geq 1$, where ${\gamma _n}(L)$ is the nth term of the lower central series of L. We also prove that $\omega u(L)$ is a residually nilpotent ideal if and only if L is residually nilpotent. Both these results remain true in characteristic 2 provided we take L to be an ordinary Lie algebra.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2975-2980
- MSC: Primary 17B35; Secondary 16S30
- DOI: https://doi.org/10.1090/S0002-9939-1995-1264829-0
- MathSciNet review: 1264829